Linear regression using Excel

Linear regression using the Excel Data Analysis Add-in... 

In the present model the pre-exponential factors and activation energies are optimised by non-linear regression using the Solver module on Microsoft Excel. The amounts of coke associated with CO2 evolution at Pi and P2 are also optimised, while a mass balance determines the coke quantity associated with CO at P5 and CO2 at P3. The oxygen partial... 

The first step is to obtain initial estimates of level and trend using linear regression. We first run a linear regression (using the Excel tool Data Data Analysis Regression) between demand and time periods. The estimate of initial level 0 is obtained as the intercept coefficient, and the trend Tq is obtained as the X variable coefficient (or the slope) in the spreadsheet Examples 1-4 Chapter 7 (there is some variation between the spreadsheet and the results shown here because of rounding). For the MP3 player data, we obtain... 

The terms Po, Pa, Pt, Pat, Paa, and Pt,t, are adjustable parameters whose values are determined by using linear regression to fit the data to the equation. Such equations are empirical models of the response surface because they have no basis in a theoretical understanding of the relationship between the response and its factors. An empirical model may provide an excellent description of the response surface over a wide range of factor levels. It is more common, however, to find that an empirical model only applies to the range of factor levels for which data have been collected. 

A non-linear regression analysis is employed using die Solver in Microsoft Excel spreadsheet to determine die values of and in die following examples. Example 1-5 (Chapter 1) involves the enzymatic reaction in the conversion of urea to ammonia and carbon dioxide and Example 11-1 deals with the interconversion of D-glyceraldehyde 3-Phosphate and dihydroxyacetone phosphate. The Solver (EXAMPLEll-l.xls and EXAMPLEll-3.xls) uses the Michaehs-Menten (MM) formula to compute v i- The residual sums of squares between Vg(,j, and v j is then calculated. Using guessed values of and the Solver uses a search optimization technique to determine MM parameters. The values of and in Example 11-1 are ... 

Concentrations of terbacil and its Metabolites A, B and C are calculated from a calibration curve for each analyte run concurrently with each sample set. The equation of the line based on the peak height of the standard versus nanograms injected is generated by least-squares linear regression analysis performed using Microsoft Excel. 

Famoxadone, IN-JS940, and IN-KZ007 residues are measured in soil (p-g kg ), sediment (p-gkg ), and water (pgL ). Quantification is based on analyte response in calibration standards and sample extract analyses determined as pg mL Calibration standard runs are analyzed before and after every 1 samples in each analytical set. Analyte quantification is based on (1) linear regression analysis of (y-axis) analyte concentration (lagmL Q and (x-axis) analyte peak area response or (2) the average response factor determined from the appropriate calibration standards. The SLOPE and INTERCEPT functions of Microsoft Excel are used to determine slope and intercept. The AVERAGE and STDEV functions of Microsoft Excel are used to determine average response factors and standard deviations. 

Problems that can be described by a multiple linear regression model (i.e., they have a single response variable, 1) can be readily solved by available software. We will demonstrate such problems can be solved by using Microsoft Excel and SigmaPlot . 

In an excellent paper, Zhao et al. [29] assembled a carefully reviewed literature set of human absorption data on 241 drugs. They showed that a linear regression model built with 5 Abraham descriptors could fit percent human absorption data reasonably well (r2 = 0.83, RMSE = 14%). The descriptors are excess molar refraction (E), polarizability (S), hydrogen bond acidity (A), hydrogen bond basicity (B), and McGowan volume (V), all related to lipophilicity, hydrophilicity, and size. In a follow-on paper, data on rat absorption for 151 drugs was collected from the literature and modeled using the Abraham descriptors [30]. A model with only descriptors A and B had r2 = 0.66, RMSE = 15%. 

We have encountered Excel s LINEST as a tool for linear regression. Unfortunately, LINEST cannot be generalised from vectors to matrices. To deal with matrices, we do not have an option but to use equations (4.59) and (4.61). It is possible to do so, but not as convenient as in Matlab. 

Li etal. discuss the use of on-line Raman spectroscopy to dynamically model the synthesis of aspirin, one of the most documented and well-understood reactions in organic chemistry. That makes it an excellent choice for building confidence in the sampling interface, Raman instrumentation, and analysis procedures. The researchers used wavelets during analysis to remove fluorescent backgrounds in the spectra and modeled the concentrations with multiple linear regression.53... 

Figure 5.20 shows a plot of the experimental temperature decay for run 1, after t = 60 min. An excellent linear regression was obtained, which means that U can be regarded as a constant value. The adiabatic temperature rise curves were calculated using Eq. (5.77) (plots are shown in Fig. 5.19). The adiabatic curves are now ready for a kinetic analysis.

To establish chiral separation method for donepezil hydrochloride enantiomers by capillary electrophoresis (CE) and to determine the two enantiomers in plasma [39], alkalized plasma was extracted by isopropa-nol-n-hexane (3 97) and L-butefeina was used as the IS. Enantioresolution was achieved using 2.5% sulfated-beta-cyclodextrin as chiral selector in 25 mmol/1 triethylammonium phosphate solution (pH 2.5) on the uncoated fused-silica capillary column (70 cm x 50 fim i.d.). The feasibility of the method to be used as quantitation of donepezil HC1 enantiomers in rabbit plasma was also investigated. Donepezil HC1 enantiomers were separated at a baseline level under the above condition. The linearity of the response was evaluated in the concentration range from 0.1 to 5 mg/1. The linear regression analysis obtained by plotting the peak area ratio (A(s)/A(i)) of the analyte to the IS versus the concentration (C) showed excellent correlation coefficient The low limit of detection was 0.05 mg/1. The inter- and intra-day precisions (RSD) were all less than 20%. Compared with chiral stationary phase by HPLC, the CE method is simple, reliable, inexpensive, and suitable for studying the stereoseletive pharmacokinetics in rabbit. 

The EC 10 was calculated using a non linear regression procedure that is available as an Excel macro at the following link http //eric.vindimian.9online.fr... 

Figure 2.3. Linear regression analysis with Excel. Simple linear regression analysis is performed with Excel using Tools -> Data Analysis -> Regression. The output is reorganized to show regression statistics, ANOVA residual plot and line fit plot (standard error in coefficients and a listing of the residues are not shown here).

A novel technique using 0.75% fluorescein isothiocyanate (FlTC)-inulin to measure inulin clearance in mice has recently been described [98-100]. We have determined that there is an excellent correlation between serum creatinine and inulin clearance in mice with ischemic AKI (unpublished data). We compared serum creatinine and GFR by linear regression and determined there was a highly significant negative correlation between serum creatinine and GFR, with Pearson r = -0.76 (P = 0.004, n = 12)... 

The quantitation of enzymes and substrates has long been of critical importance in clinical chemistry, since metabolic levels of a variety of species are known to be associated with certain disease states. Enzymatic methods may be used in complex matrices, such as serum or urine, due to the high selectivity of enzymes for their natural substrates. Because of this selectivity, enzymatic assays are also used in chemical and biochemical research. This chapter considers quantitative experimental methods, the biochemical species that is being measured, how the measurement is made, and how experimental data relate to concentration. This chapter assumes familiarity with the principles of spectroscopic (absorbance, fluorescence, chemi-and bioluminescence, nephelometry, and turbidimetry), electrochemical (poten-tiometry and amperometry), calorimetry, and radiochemical methods. For an excellent coverage of these topics, the student is referred to Daniel C. Harris, Quantitative Chemical Analysis (6th ed.). In addition, statistical terms and methods, such as detection limit, signal-to-noise ratio (S/N), sensitivity, relative standard deviation (RSD), and linear regression are assumed familiar Chapter 16 in this volume discusses statistical parameters. 

T Spreadsheet Summary In the final three exercises in Chapter 7 of —I Applications of Microsoft Excel in Analytical Chemistry, we first use Excel to plot a simple distribution of species diagram (a plot) for a weak acid. Then, the first and second derivatives of the titration curve are plotted to better determine the titration end point. A combination plot is produced that simultaneously displays the pH versus volume curve and the second-derivative curve. Finally, a Gran plot is explored for locating the end point by a linear regression procedure. 

Spreadsheet Summary In Chapter 15 of Applications of Microsoft Excel in Analytical Chemistry, capillary electrophoresis data are used to determine the mobilities of inorganic ions. Measurements of the anival times of ions at the detector are used with the known mobility of Na" to determine mobilities. Capillary electrophoresis results are also used to determine pK values of several weak organic acids. Linear regression analysis is used to find the pK values from measurements of arrival times at different buffer pH values. 

Linear analysis was carried out using Excel and the non linear regression analysis was carried out with NLREG (Version 5.2 Phillip H. Sherrod 1991-2001). 

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